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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2013/2014 -
- ARCHIVE as at 1 September 2013 for reference only
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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Stochastic Analysis in Finance I (MATH11076)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityNot available to visiting students
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) Credits7.5
Home subject areaMathematics Other subject areaFinancial Mathematics
Course website None Taught in Gaelic?No
Course descriptionThis course aims to provide a good and rigorous understanding of the mathematics used in derivative pricing and to enable students to understand where the assumptions in the models break down.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Other requirements MSc Financial Mathematics and MSc Financial Modelling and Optimization students only.
Additional Costs None
Course Delivery Information
Delivery period: 2013/14 Semester 1, Not available to visiting students (SS1) Learn enabled:  Yes Quota:  None
Web Timetable Web Timetable
Course Start Date 16/09/2013
Breakdown of Learning and Teaching activities (Further Info) Total Hours: 75 ( Lecture Hours 24, Summative Assessment Hours 1.5, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 48 )
Additional Notes
Breakdown of Assessment Methods (Further Info) Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Exam Information
Exam Diet Paper Name Hours:Minutes
Main Exam Diet S2 (April/May)3:00
Summary of Intended Learning Outcomes
- be able to demonstrate an understanding of continuous time stochastic processes
- know the main results and basic applications of stochastic Ito calculus
- be able to understanding stochastic differential equations (SDE's)
- be able to understanding equivalent measures and in particular Girsanov's theorem
- conceptual understanding of martingales in continuous time.
- conceptual understanding of the stochastic Ito integral and It's formula.
Assessment Information
See 'Breakdown of Assessment Methods' and 'Additional Notes', above.
Special Arrangements
MSc Financial Mathematics and MSc Financial Modelling and Optimization students only.
Additional Information
Academic description Not entered
Syllabus Continuous time processes: basic ideas, filtration, conditional expectation, stopping times.
Continuous parameter martingales, sub- and super-martingales, martingale inequalities, optional sampling.
Wiener martingale, stochastic integral, the Itô calculus and some applications.
Multi-dimensional Wiener process, multi-dimensional Itô formula.
Stochastic differential equations
Change of measure, Girsanov's theorem, equivalent martingale measures and arbitrage.
Representation of martingales and the Ornstein-Uhlenbeck process.
Transferable skills Not entered
Reading list Karatzas, I. & Shreve, S. (1988). Brownian Motion and Stochastic Calculus. Springer.
Baxter, M. & Rennie, A. (1996). Financial Calculus. CUP.
Etheridge, A. (2002). A Course in Financial Calculus. CUP.
Lamberton, D. & Lapeyre, B. (1996). Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall.
Study Abroad Not Applicable.
Study Pattern Not entered
KeywordsSAF I
Contacts
Course organiserProf Istvan Gyongy
Tel: (0131 6)50 5945
Email: I.Gyongy@ed.ac.uk
Course secretaryMrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk
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